MANCHESTER, N.H. — Seeking to build momentum after a solid debate performance this week, President Obama continued a whirlwind tour of battleground states Thursday by urging 6,000 boisterous supporters here to turn their cheers into votes on Nov. 6.

Under a canopy of brilliant fall foliage in a downtown park, Obama hit Romney on jobs, taxes, energy, and women’s issues in crowd-rousing broadsides that echoed the attacks he unleashed at Hofstra University.

Obama assailed Romney for not specifying what deductions and loopholes he would eliminate to offset the revenue lost in his tax-cut plan, which Democrats have said would cost $5 trillion over a decade.

“I’m going to give you a little tip,” Obama said to laughter. “When a politician tells you he’s going to wait until after the election [to release details], it’s not because their plan is so good that they don’t want to spoil the secret.”

When the crowd jeered, the president quickly cut them off: “Don’t boo, vote!”

Following the rally, the Romney campaign said the president had offered familiar, ineffective prescriptions that will not improve the economy.

“The president is out of new ideas, out of time, and out of excuses to explain his failed leadership and broken promises,” said Ryan Williams, a Romney campaign spokesman.

Romney was not actively campaigning Thursday.

Although Obama performed much better at Hofstra than he did in the first debate in Denver, polls in several battleground states have been mixed. On Thursday, a national Gallup survey of likely voters showed Romney leading the president, 52 percent to 45 percent.

However, an NBC/Wall Street Journal/Marist University poll Thursday showed Obama maintaining his 8-point lead in Iowa from last month. In Wisconsin, Obama’s lead increased one percentage point from last month, to six, according to the poll.

Also Thursday, the Orlando Sentinel, which endorsed Obama in 2008, backed Romney. The paper circulates in an area where many Florida elections are decided, along a crucial Interstate 4 corridor.

In New Hampshire, recent polls have shown a deadlocked race after many weeks in which Obama had led.

Despite those numbers, the president appeared buoyant as he bounded up to the lectern with his white shirtsleeves rolled up, waved and smiled broadly.

Obama mocked Romney’s five-point economic plan as a “one-point plan” that would benefit the wealthy and reinstate a trickle-down economy.

“Folks at the top get to play with a different set of rules than you do,” Obama said of Romney’s proposals. “It’s the same philosophy that’s been squeezing middle-class families for more than a decade. It’s the same philosophy that got us into this mess.”

In an effort to retain his margin among women, which appears to be slipping, Obama cited the pay-equity law he signed in 2009, known as the Lilly Ledbetter act.

“Governor Romney still won’t say whether or not he supported the law to protect that right,” Obama said.

He also tried to link Romney to the New Hampshire Legislature, whose Republican-led chambers have considered several restrictive measures on abortion, contraceptives, and other reproductive issues.

“You’ve got a state legislature up here that sometimes acts like it knows better when it comes to women’s own health-care decisions,” Obama said. “My opponent has got the same approach.”

Obama said he is looking forward to the third and last debate, scheduled for Monday in Boca Raton, Fla., where foreign policy will be the focus.

One of the most pointed clashes at Hofstra involved Romney’s criticism that the president had failed for two weeks to label the deadly assault in Benghazi, Libya, which killed the US ambassador and three other Americans, as an act of terrorism.

Obama sternly dismissed that assertion during the debate, saying he had called the attack a terrorist act the following day, and described Romney’s implication that he had put campaign politics ahead of an investigation into the killings as “offensive.”

In Manchester, some Obama supporters said they are concerned about the tightening race.

“I don’t see enough Obama signs, so I’m going to get a bumper sticker,” said Dr. Margaret Flynn, 48, an endocrinologist from Nashua who attended the rally with her 10-year-old daughter, Clara Chung.

“I think we’re all one job away from having no health insurance,” Flynn said. “I don’t want to see Romney get elected and destroy” the health-care act passed under Obama.

US Senator Jeanne Shaheen, who spoke before the president, stressed the importance of New Hampshire’s four electoral votes.

“This election is so critical to our future. What happens on Nov. 6 will determine whether we continue to have a country with opportunities for all Americans, where everybody has the ability to play by the rules and get ahead,” Shaheen said. “You all know this race is close.”

Carol Buchanan, 68, of Concord, N.H., said she remains confident that Obama will win.

“I think he still has a good chance,” Buchanan said. However, her friend Jane McNeil of Concord, Mass., quickly added: “We hope he has a good chance! I don’t think the other choice is very good.”

On the television show “The View,” Ann Romney said Thursday that if Romney loses, he “absolutely” will not run again. His decision to seek the White House once more, following his defeat in the 2008 Republican primaries, has been a “very hard thing” for the family to endure, she told “The View.”

Ann Romney said she agreed to another campaign because she believes her husband can restore the country to economic prosperity.

Josh Romney, one of the couple’s five sons, was asked about his brother Tagg’s statement following the debate that he wanted to “take a swing” at the president.

Josh, as someone who has been hit by Tagg, said the president does not need to be concerned.

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